Rectification of AC signals into DC signals is one of the simplest and the most important processes in electronics. In electronics it is achieved in two stages: polarity elimination followed by low-pass filtering.
In optics, spatial rectification can be achieved through similar steps: phase elimination and spatial low pass filtering. It has considerable importance in optical signal processing for such applications as beam cleanup, injection of the output of multimode fibers into single mode fibers, and amplification of the output of a single diode laser by an array of phase-locked lasers.
In contrast to the use of diodes for polarity elimination in rectification for serial electronics, we use quadratic processing to demonstrate optical phase elimination. Quadratic or square law receivers are often used in detecting signals in the presence of signal-dependent or multiplicative noise and in processing non-Gaussian signals. For detecting Gaussian signals in non-Gaussian noise, the limiting square law receiver is the optimal receiver
In accordance with the present invention we illustrate the mechanism of rectification using photorefractive two-beam coupling. We present a computer simulation of the optical rectification and its relationship to beam cleanup experiments. We also propose a new technique for dealing with multiplicative complex speckle noise on imaged amplitude objects. This method uses the limiting square law processing associated with two-beam coupling to convert complex multiplicative noise into additive noise. Experimental results are presented accompanied by computer simulations showing improvements of the signal to noise ratio (SNR) due to the associated dynamic range compression. This SNR can be further improved by subsequent nonlinear filtering in the Fourier plane. Finally, we present a general method for the reduction of multiplicative noise in optical images.
This method generalizes the homomorphic filtering technique by the principle of compansion (compression and expansion). Compansion is a well established technique in electronics for reducing noise is serial signals. We believe that this is the first time that the compansion principle has been introduced in optical signal processing.